Question

Let A = {a, b}. List all relations on A and find their number.

Answer 1

Here, A = {a, b}

We know that,

Number of relations $=2^{mn}$

$=2^{2.2}$

$=24$

$=16$

Number of relation on A = 16

Relations on A are given by

R = {a, a}, {a, b}, {b, a}, {b, b}

{(a, a), (a, b)}, {(a, a), (b, a)}, {(a, a), (b, b)}

{(a, b), (b, a)}, {(a, b), (b, b)}, {(b, a), (b, b)},

{(a, a), (a, b)}, {(b, a), (a, b)}, {(b, a), (b, b)}

{(b, a), (b, b)}, {(a, a), (b, b)}, {(a, a), (a, b)}

{(a, a), (b, a)}, {(b, b), (a, a)}, {(b, a), (b, b)}